Mister Exam

Other calculators

x^2-x-90=0 equation

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src] 
 2             
x  - x - 90 = 0
(x2−x)−90=0\left(x^{2} - x\right) - 90 = 0
Simplify
Detail solution
This equation is of the form
a*x^2 + b*x + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=1a = 1
b=−1b = -1
c=−90c = -90
, then
D = b^2 - 4 * a * c = 

(-1)^2 - 4 * (1) * (-90) = 361

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
x1=10x_{1} = 10
x2=−9x_{2} = -9
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−1p = -1
q=caq = \frac{c}{a}
q=−90q = -90
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=1x_{1} + x_{2} = 1
x1x2=−90x_{1} x_{2} = -90
Rapid solution [src] 
x1 = -9
x1=−9x_{1} = -9 
x2 = 10
x2=10x_{2} = 10 
x2 = 10
Sum and product of roots [src] 
sum
-9 + 10
−9+10-9 + 10 
=
1
11 
product
-9*10
−90- 90 
=
-90
−90-90 
-90
Numerical answer [src] 
x1 = -9.0
x2 = 10.0
x2 = 10.0
    © Mister Exam – Calculator